Differential Operators on Varieties with a Quotient Subvariety Original Research Article

A finite group G acts on a smooth affine variety Spec A, leaving stable a closed subvariety Spec A/J. The ring of functions on the variety obtained from Spec A by replacing Spec A/J by its quotient (Spec A/J)/G and leaving the complement Spec A\Spec A/J unchanged is AG + J. For reasonable G-actions the ring of differential operators image(AG + J) has a unique minimal non-zero ideal, Jimage(A), with the factor isomorphic to image(A/J)G. Particular cases of this construction are considered with emphasis on the problem of when differential operators extend from (A/J)G to A/J.